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Formation and mechanical characterization of ionically crosslinked membranes at oil–water interfaces Wa Yuan, Evan J. Laprade, Kevin J. Henderson and Kenneth R. Shull* Here we report on the preparation and mechanical characterization of a 2-D self-assembled membrane formed by ionically crosslinking the polyelectrolyte parts of a gradient amphiphilic copolymer at oil and water interfaces. To fabricate these membranes, chloroform solutions of styrene–acrylic acid copolymers were suspended as pendant drops in an aqueous embedding phase. Due to the amphiphilic nature of these molecules, the copolymer chains migrate to the oil–water interface creating an interfacial layer. Upon the addition of zinc acetate to the embedding phase, crosslinks between copolymer molecules are formed via zinc–carboxylate complexes. While ionically crosslinked block copolymer membranes were critically damaged after one expansion cycle, ionically crosslinked gradient copolymers formed durable membranes that maintained their physical integrity through multiple expansion–compression–expansion cycles. This difference in mechanical behavior is attributed to the fact that gradient copolymers are more effective interfacial modifiers and have a significantly different molecular alignment at the oil–water interface. Additionally by changing the incubation time from 20 to 30 minutes, the low-strain dilatational modulus of these membranes was significantly increased due to
Received 16th July 2013 Accepted 25th October 2013
higher interfacial coverage and crosslinking density. Longer incubation times also led to a distinct yield point and plastic deformation behavior at larger strains. Further mechanical characterization of the
DOI: 10.1039/c3sm51943k
membranes showed that they can be quite robust and that by replacing the internal oil phase with an
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aqueous solution, future testing of membrane filtration and permeation may be possible.
1. Introduction Ionically crosslinked networks are oen incorporated into covalently crosslinked polymers to enhance their mechanical and transport properties.1–4 In polymer bulk gels for instance, the addition of a second, tightly cross-linked network assists in broadening the fracture zone and maximizing dissipation, creating so materials with fracture energies comparable to or exceeding that of natural biomaterials.1 Additionally, the reversibility of these bonds provides these gels with a remarkable ability to recover aer plastic deformation, giving them a self-healing character.2 Ionic crosslinking of two dimensional structures is equally attractive, as it can be used to tailor the membrane permeability and permselectivity for liquid phase transport applications. In recent work, these lms have increasingly been targeted as membranes for liquid mixture separation,5,6 drug delivery7 and fuel cells.8–10 Looking towards these goals, we introduce a simple way of preparing and mechanically characterizing free standing ionically crosslinked polymer membranes. Northwestern University Materials Science and Engineering, 2220 Campus Drive, Evanston, Illinois, USA. E-mail: [email protected]; Fax: +1 8474917820; Tel: +1 8474671752
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The most frequently used technique to produce ionic crosslinking is by complexation of multi-valent cations and carboxylate ligands, in what is predominantly an electro-static interaction. In our experiments, pendant drop membranes
Fig. 1 Formation of ionically crosslinked interfacial layers: (left) gradient copolymers dissolved in chloroform adsorb onto the interface of a pendant drop at the tip of a capillary needle. The embedding phase is pure water. The inset shows an idealized orientation of gradient copolymers at the oil–water interface. (right) Zinc acetate solution is added to the aqueous embedding phase. The inset shows divalent ion-carboxylate ligand complexing at the interface, creating an ionically crosslinked membrane.
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2.
Materials and methods
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2.1. Materials
Fig. 2 (a) Schematic structure of a styrene/acrylic acid gradient copolymer. Carboxylate ligands replace aqua ligands in the inner sphere of a Zn ionic complex. Schematic structure of styrene (b) and (c) acrylic acid.
were formed through zinc(II) crosslinking of an amphiphilic styrene/acrylic acid gradient copolymer (Fig. 2) at an oil–water interface as shown in Fig. 1. The pendant drop technique is a commonly used method for characterizing the mechanical properties of two dimensional structures that self-assemble at uid–uid interfaces. While being conceptually more complex than at interface techniques,11–13 a pendant drop technique can offer several important advantages due to its small reagent volumes and rapid equilibration times. The interfacial tension between the drop and the embedding phase can be obtained by analyzing the drop shape, and changing the drop volume allows one to mechanically characterize the interface. The amphiphilic copolymers used here to form crosslinked membranes are referred to as gradient copolymers (Fig. 2). They exhibit a gradual change of composition along the backbone,14 which leads to lower repulsion forces distributed along the chain. It has been shown previously that the molecular structure of gradient copolymers results in a larger critical micelle concentration in polymer blends15–17 and molecular alignment at the oil–water interface that differs signicantly from traditional block copolymers.18 Our work suggests that copolymer membrane formation is facilitated by the reduction of these kinetic barriers and by the specic details of the molecular organization at the interface before crosslinking. In this paper we begin by discussing the materials and methods for fabricating ionically crosslinked pendant drops. Then we summarize the mechanics of the pendant drop geometry, and provide the background necessary to analyze both uid and elastic interfaces. Next we model an ionically crosslinked drop with both analyses, evaluating the t quality and principal tension predictions. The availability of these models puts us in a position to characterize the mechanical behavior of these membranes, look at the effect of processing conditions, and discuss their self-healing ability. Lastly we present preliminary results highlighting how the robust nature of this technique could be used to look at transport through these crosslinked interfaces.
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Styrene–acrylic acid (S/AA) gradient copolymers were synthesized as previously described18 using semi-batch nitroxide mediated controlled radical polymerization (NM-CRP) from the unimolecular initiator alkoxyamine 29 (2,2,5-trimethyl-3(1-phenylethoxy)-4- phenyl-3-azahexane).19 The PS/PtBA precursor copolymers were recovered by cycles of precipitation into methanol and dissolution into tetrahydrofuran before drying under vacuum. For comparison a block copolymer with similar molecular weight was also prepared, using sequential, batch NM-CRP. The nal products were labeled as G92 (Mn ¼ 91 800 g mol1, styrene fraction ¼ 0.55) and B89 (Mn ¼ 88 700 g mol1, styrene fraction ¼ 0.69), according to the copolymer type and number average molecular weight. The nal apparent molecular weights (MWs) and cumulative styrene mole fractions (FS) for the two types of copolymers used for this study are summarized in Table 1. Both copolymers were dissolved in chloroform (CHROMASOLV PLUS, FOR HPLC) at a concentration of 0.02 mg mL1. Dihydrate zinc acetate (as received, Sigma Aldrich) and pure water (A. C. S. REAGENT, Sigma Aldrich) were used to prepare 400 mM zinc acetate solutions. These solutions were buffered with acidic acid to a nal pH of 6, conrmed using a WTW Portable pH Tester, Model 20. 2.2. Drop shape analysis system A commercial drop shape tensiometer (Kr¨ uss DSA 100) was used to image the pendant drop prole. The drop shape analysis video was analyzed with a custom written MATLAB (Mathworks) pendant drop mechanical analysis, outlined in Section 3. The drop volume was controlled via a motor driven syringe system. 2.3. Pendant drop membrane fabrication Interfacial layers were investigated using the pendant drop method and drop-shape analysis (DSA). A 4–6 ml pendant drop of chloroform containing the desired copolymer was formed at the end of the capillary needle (diameter ¼ 0.914 mm) inside a water lled glass cuvette (cuvette dimensions ¼ 1 cm 1 cm 5 cm). Once the pendant drop was formed, it was xed at the initial volume for a period of time (referred to here as the “incubation period”) to allow the copolymers to migrate to the oil and water interface. Aer this incubation period, zinc acetate
Summary of molecular characterization data for gradient (G) and diblock (B) S/AA copolymers
Table 1
Sample
Fs
Mna (g mol1)
PDIa
G92 B89
0.55 0.69
91 800b 88 700c
1.48b 1.79b
a Mn and PDI data based on S/tBA copolymers. b The apparent value characterized relative to PS standards by GPC with THF as an eluent. c The Mn value was determined from the Mn of the PtBA macroinitiator and the Fs value.
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solution was added to the aqueous imbedding phase to create carboxylate ligand complexation at the interface. The nal concentration of zinc acetate in the aqueous phase was approximately 40 mM. Aer the addition of zinc acetate, the drop was held for approximately ve minutes to form an ionically crosslinked interface. Immediately following this period, the drop volume was decreased slightly to test the formation of the membrane, indicated by wrinkling of the interface. Aer the drop was re-expanded back to the original size, a set of cycles were carried out following a routine of expansion– compression–expansion. Drops were expanded to a 40% increase in interfacial area (relative to the initial drop surface area), compressed to a 20% reduction, and then re-expanded back to the original size. The time between the end of one expansion–compression–expansion cycle and the start of the next was approximately three minutes. All experiments were performed at a xed ow rate of 0.4 mL min1. Before and aer each new experiment, the glass cuvette was thoroughly washed with acetone and water, while the needles and glass syringe were washed with acetone and chloroform. Fig. 3 shows representative images at different stages of expansion and compression for a crosslinked G92 copolymer membrane. We note that the wrinkling wavelength observed during compression is approximately 35–40 mm for the smallest observable wrinkles, and at larger compressions these small wrinkles became larger folds with a wavelength of approximately 100 mm. These wrinkle wavelengths are quite similar to those observed by Erni et al.20 for oil–water emulsion drops exhibiting shear elasticity.
3.
Membrane mechanics
3.1. Theoretical background DSA is most commonly used to measure the interfacial tension between two immiscible uids, but has increasingly been employed to characterize the mechanical behavior of molecular structures that self-assemble at these interfaces.20–24 General theoretical frameworks that encompass these solid-like interfaces have been summarized recently,25,26 here we follow the formulation given by Carvajal et al.26
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Fig. 4 Schematic representation of an axisymmetric pendant drop.
In Fig. 4, we dene a coordinate system for the pendant drop geometry with its origin at the drop apex. The arc length of the interface between the two phases s runs from the apex (s ¼ 0) to the capillary edge (s ¼ l), where l is the total integrated arc length. The shape of the pendant drop interface is dened by its principal curvatures Rx and Rf, the curvatures in the r z plane and in the azimuthal direction respectively. The principal curvatures are dened as ds da
(1)
r sin a
(2)
Rx ¼ Rf ¼
where the quantity a(s) is the angle between the tangent to the interface at [r(s), z(s)] and the radial axis. In the most general case of an elastic or solid-like interface, the pendant drop geometry is governed by force balances in the direction normal to the interface, and along the x principal direction (a force balance in the f direction is satised by the axisymmetry of the problem). From the normal force balance one can derive the Young–Laplace relationship: DP ¼
Tx Tf þ Rx Rf
where the principal tensions, Tx and Tf, and local curvatures balance the pressure difference across the interface, DP. It can be shown that the mechanical equilibrium equation for the x direction is given by: d ðTx rÞ ¼ Tf dr
Images of the crosslinked G92 copolymer membrane (20 minute incubation) during the 1st expansion–compression–expansion cycle. The left image corresponds to A/A0 ¼ 1, where A0 is the drop surface area at the beginning of the cycle. The center image corresponds to A/A0 ¼ 1.39 (the maximum surface area during the cycle). The right image corresponds to a deep compressed state (A/A0 ¼ 0.81) where wrinkling can be observed in the upper portion of the drop interface. Fig. 3
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(3)
(4)
In the case of a purely uid interface, which is unable to support shear stresses, the principal tensions are spatially uniform and equal, Tx ¼ Tf ¼ g. Eqn (4) is automatically satised, and the interfacial tension can be measured by simply tting the Young–Laplace equation to the drop prole. An elastic or solid interface presents a more complicated situation where the principal tensions are no longer isotropic and instead will depend on the local in-plane principal strains, lx and lf. For an elastic interface we assume that the principal tensions consist of a pretension component g0 , equal to the interfacial tension of the pendant drop in the undeformed state, and an elastic component, which is determined by the strain energy per unit area of the undeformed membrane, U.
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T x ¼ g0 þ
1 vU lf vlx
(5)
T f ¼ g0 þ
1 vU lx vlf
(6)
A neo-Hookean strain energy function is commonly chosen as a general description of elasticity,27 and here we use it to derive the following expressions for the principal tensions: ! Eh0 lx 1 0 Tx ¼ g þ (7) 3 lf lx 3 lf 3 Eh0 Tf ¼ g þ 3 0
lf 1 lx lx 3 lf 3
! (8)
where Eh0 is the low-strain dilatational modulus, E is Young’s elastic modulus, and h0 is the undeformed thickness of the membrane. Eqn (7) and (8) were derived under the assumption of incompressibility. In Section 3.4 we utilize both the uid interface analysis (eqn (3)) and the elastic interface analysis (eqn (3)–(8)) to characterize the mechanical behavior of a crosslinked gradient copolymer pendant drop. 3.2. Fluid interface tting Isotropic interfacial tension values were determined using a modied version of the Young–Laplace tting routine previously described by Carvajal et al.26 To briey summarize, eqn (1)–(3) are combined with the geometrical relationships, dr/ds ¼ cos a and dz/ds ¼ sin a, to give three coupled rst order differential equations (for a, r and z) that describe the pendant drop’s conguration. We specify ve boundary conditions: three at the drop apex and two at the capillary needle edge. In order for all ve boundary conditions to be met, two parameters must be allowed to oat. These parameters are the interfacial tension, g, and the pressure at the apex, P0. A custom MATLAB script was used to digitize the drop prole, solve the differential equations, and adjust the parameters to determine which value of g minimizes the error, Lres, in prole tting. This error is dened in the following way: Lres ¼
N 1 X di ; NRm i¼1
(9)
where di is the normal distance between the model and the experimental prole at each model prole point (r(i), z(i)), Rm is the radius of the membrane holder, and N is the total number of points along the prole. Note that Lres is the average distance between the actual drop prole and the t to the droplet shape from the solution to the equations in the previous section, normalized by Rm. 3.3. Elastic interface tting For the elastic case we need to solve a total of four differential equations, for a, z lx, and lf. There are a total of six boundary conditions to be met, so two parameters must be allowed to
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oat, and these parameters are the pressure at the apex of the deformed membrane, and Eh0, the low strain dilatational modulus. Our use of Eh0 as an adjustable parameter is not a rigorous treatment of viscoelasticity, but this method provides a simple rst order approximation of the time-dependent modulus of the membranes. To analyze an elastic interface we make the assumption that a pendant drop with a liquid-like interfacial layer has undergone crosslinking, forming an elastic membrane at the interface. This undeformed, yet crosslinked pendant drop is dened as the reference conguration. It is assumed that in this undeformed state, the principal tensions are spatially uniform and equal to one another, Tx ¼ Tf ¼ g0 . Subsequent deformation of the drop changes the local values of lx and lf and therefore the elastic contributions to the principal tensions. We begin by determining g0 , analyzing an image of the undeformed drop with the uid interface analysis. Aer determining g0 , the elastic drop analysis can be used to model the deformation of drop starting with expansion. A custom MATLAB script was used to digitize the drop prole, solve the differential equations, and adjust the parameters to minimize the error, Lres.
3.4. Fluid and elastic interface analysis comparison The uid to elastic transition of pendant drop interfaces can be monitored by examining the error in tting the Young–Laplace equation to the interface shape.23,25,28 As the drop becomes more solid-like there will be an increase in the error that can provide a signature of the formation of an elastic interface with nonuniform tension. The use of an approximate “uid interface” model that assumes a uniform, isotropic tension is motivated by the simplicity of the tting routines that are generally available for commercial pendant drop instruments. An important question that needs to be addressed in these situations is how closely this uid interface analysis approximates the true interfacial tension. In this section we examine the agreement between the elastic and uid interface analyses for our crosslinked pendant drops, specically looking at the quality of the prole ts and at the magnitude and spatial variation of the interfacial tensions. Following the procedure outlined in Sections 3.2 and 3.3, uid and elastic interface analyses were applied to the expansion and compression cycle of a G92 gradient copolymer pendant drop. During the 20 minute incubation period, the drop interface has a uid-like character, and we expect excellent agreement between the interface shape and the Young–Laplace solution. We can use the average value of the tting error in this regime (Lres ¼ 0.0025), as a reference for what constitutes a quality t. In Fig. 5, this average tting error for the uncrosslinked drop is plotted as a solid black line, along with the tting error for the uid and elastic interface analyses during the expansion and compression of the crosslinked G92 gradient copolymer pendant drop. Both analyses produce comparable residuals over the majority of deformations. In both cases the error is comparable to our reference value until the drop is compressed back to an areal dilatation of A/A0 ¼ 1, where A is the actual interfacial area and A0 is the original interfacial area
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Fig. 5 Left axis: the fitting error, Lres, for the fluid and elastic analysis fits to the pendant drop profile. This measurement was the first expansion–compression cycle of an ionically crosslinked G92 membrane (20 minute incubation period). The solid black line corresponds to the average fitting error for the uncrosslinked G92 pendant drop. Right axis: areal dilatation versus experiment time.
for that specic cycle. Further compression results in poor tting for both cases, particularly as the membrane begins to wrinkle (A/A0 < 0.95), and the tting error sharply increases. As
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neither model correctly interprets the tensions in this regime, we restrict our analysis to A/A0 > 0.95 in the work that follows. The prole ts and local residuals at interfacial area extensions A/A0 ¼ 1.09 (time ¼ 110 s) and A/A0 ¼ 1.29 (time ¼ 548 s) are shown in Fig. 6a, c and (d)–(f) respectively. For both of these deformations the uid interface, elastic interface, and experimental proles are nearly indistinguishable from one another (Fig. 6a and d) and small differences only become clear when looking at the local residuals (Fig. 6b and e). More signicant differences between the models are evident in the principal tension behavior, Fig. 6c and f, particularly in the spatial distribution of the principal tensions. The additional boundary conditions for the elastic interface analysis lead to an anisotropic strain state, with the boundary condition lx(s ¼ 0) ¼ lf(s ¼ 0) forcing equibiaxial tension at the drop apex and the boundary condition lf(s ¼ l) ¼ 1 diverging the principal tensions at the capillary edge. Our analysis of the G92 crosslinked interface shows a small deviation between the elastic tensions and g, as depicted in Fig. 7 and 8. Interestingly, despite the very close agreement between the uid and elastic prole shapes, the interfacial tension, g, does not necessarily fall somewhere in between the predictions for Tx and Tf. At the apex, the uid analysis slightly overestimates the tension, as shown in Fig. 7, and similarly
Fluid and elastic interface analysis results for the first expansion–compression cycle of a G92 copolymer membrane (20 minute incubation time). Plots (a–c) correspond to A/A0 ¼ 1.09, time ¼ 110 s. Plots (d–f) correspond to A/A0 ¼ 1.29, time ¼ 548 s. Left plots (a and d) show the measured membrane profile prior to expansion (undeformed membrane, gray solid line) and the experimentally measured membrane profile at A/A0 (deformed membrane, green solid line). The fluid model fit to the deformed membrane profile (black dashed line), and the elastic model fit to the deformed membrane profile (blue dashed line) are nearly indistinguishable from themselves and the measured deformed membrane profile. The center plot (b and e) shows the residual errors di/Rm, along the membrane profile from the fluid and elastic interface analysis. Right plots (c and f) compare the principal tensions given by the elastic analysis to the interfacial tension, g, measured by the fluid analysis. Note that these x-axes run from the membrane apex, s/l ¼ 0, to the clamp edge, s/l ¼ 1. Fig. 6
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deviations between the elastic and uid tting routines to be more pronounced. We used the uid model to analyze all of the data discussed in the following sections.
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4. Results and discussion 4.1. Block and gradient copolymer membrane deformation
Fig. 7 Apex interfacial tension (IFT) plotted as a function of areal dilatation for the first expansion–compression cycle of a crosslinked G92 copolymer membrane (20 minute incubation time). The solid arrow represents the direction of the curve during expansion and the dashed arrow represents the direction of the curve during compression. The fluid interface analysis was used to calculate g, and the elastic interface analysis was used to calculate the tension at the apex. Note Tx(s ¼ 0) ¼ Tf(s ¼ 0) ¼ Tapex.
As described above, the G92 gradient copolymer was dissolved in chloroform at a concentration of 0.02 mg mL1, and this solution was used to form a pendant drop at the tip of a capillary needle submerged in water. During the incubation period the interfacial tension decreased signicantly from that of pure chloroform/water (32.8 mN m1). Aer a 20 minute incubation period g decreased approximately to 17 mN m1, and aer a 30 minute incubation period g decreased approximately to 10 mN m1. Additionally during this incubation time, the initially clear drop became more cloudy in appearance. Aer the addition of zinc acetate, the G92 drop was compressed and wrinkling was clearly observed, indicating the formation of a crosslinked membrane at the oil–water interface. In each subsequent expansion–compression cycle wrinkling was always observed during compression. Fig. 9 shows a comparison between an expansion–compression cycle of interfaces with and without cross-linking on exposure to zinc acetate. Droplets formed by B89 on the other hand showed a significantly smaller decrease in interfacial tension in these incubation periods compared to G92 gradient copolymers. This observation was consistent with our previous results which showed that in a limited time scale block copolymers are less efficient at going to the oil–water interface due to kinetic barriers associated with micelle aggregation in the chloroform phase.18 The coverage of copolymers at the interface was not sufficient to form a uniform membrane, and thus droplets formed by B89 did not show a clear sign of wrinkling during compression. To further compare, we increased the concentration of B89 solution to 0.1 mg mL1 and extended the
Fig. 8 Interfacial tension (IFT) at the capillary edge (z(s ¼ 1) ¼ d) plotted as a function of areal dilatation for the first expansion–compression cycle of a crosslinked G92 copolymer membrane (20 minute incubation time). The fluid interface analysis was used to calculate g, and the elastic interface analysis was used to calculate the principal tensions at the capillary edge.
overestimates Tf at the capillary edge, as shown in Fig. 8. The best agreement between the uid and elastic analyses can be found in their prediction of Tx at the capillary edge, where the tensions track closely until A/A0 z 1.08, at which point the tting error for both analyses begins to signicantly increase. While the deviations between the elastic and uid interface analyses are non-trivial, a good agreement exists between the two, particularly for g and Tx at z ¼ d. These observations suggest that in our case, the simpler, and more tractable uid analysis can provide a useful approximation of the interfacial tension. For more strongly crosslinked interfaces with higher stiffness and less healing capability,25 one would expect the
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Fig. 9 Comparison of interfacial tension behavior between G92 uncrosslinked (blue circles) and crosslinked (black squares) layers during expansion–compression. Dashed arrows represent the direction of curve during compression and solid arrows represent the direction of the curve during expansion.
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for new crosslinks to form. The deformation shown in Fig. 9 is a characteristic cycle (in this case the rst cycle) for a G92 membrane incubated for 20 minutes. At small strains there is an initial linear section where we can characterize the stiffness of these membranes by measuring the dilatational modulus, k, dened as follows: dg k ¼ A0 (10) dA
Schematic illustration of the proposed interfacial structure evolution of crosslinked block and gradient copolymer membranes under an applied tensile force.
Fig. 10
incubation time to 3 hours. Under this condition the interface did show a sign of wrinkling during the compression process, indicating the formation of a crosslinked membrane. However, when we expanded the drop by 20% and re-compressed it, the wrinkling phenomenon was no longer observed, indicating damage of the membrane during expansion. Fig. 10 shows a schematic representation of the proposed cross-linking processes for the two types of copolymers. For block copolymers, the junction points between blocks of the hydrophobic and hydrophilic monomers are localized at the oil–water interface, forming a brush-like structure. The addition of zinc ions to the aqueous phase crosslinks this entangled brush layer. When the interface is expanded, a tensile force is applied to the crosslinked layer pulling the block copolymers apart, and breaking the membrane. Gradient copolymers on the other hand have multiple hydrophilic/hydrophobic junction points along the chain which may result in a more “parallel” structure, with the molecules laterally extended along the interface.17,18,29 Aer the addition of zinc these “parallel” chains form a more complex network of intermolecular cross-links, resulting in the formation of a stronger membrane. When this membrane is placed under a similar tensile force, the “parallel” molecules do not simply detach from each other, but rather extend and uncoil. This helps maintaining the physical integrity of the membrane and enables the membrane to be expanded to twice its original area.
The small strain stiffness for this rst expansion cycle was k z 47 mN m1, signicantly higher than that of the uncrosslinked layer, k z 14 mN m1. While the dilatational modulus remains fairly constant for the uncrosslinked interface in Fig. 7, as the membrane is expanded to larger strains the slope of the interfacial tension curve decreases. Our explanation for this soening behavior is a combination of damage to the crosslinked network (local crosslink fracture, rather than catastrophic failure), and also adsorption of the uncrosslinked copolymer onto the expanded interface. As the drop is compressed back to its original size, uncrosslinked copolymer de-adsorption from the interface contributes to the signicant hysteresis between the expansion and compression cycles. Aer the drop is compressed back to its original interfacial area, the three minute incubation time in between cycles allows the fractured interface to repair and for new crosslinks to form. If we consider the beginning of each cycle to be like the formation of a new crosslinked membrane, we can characterize the excess surface stress, s, for each cycle: s ¼ g g0
(11)
where g0 is the interfacial tension at the beginning of each specic cycle. In Fig. 11, s is plotted as a function of A/A0 for the rst four deformation cycles of the crosslinked G92 copolymer aer a 20 minute incubation. The small strain expansion is comparable for all cycles, characterized by an average k value of 45 mN m1. The reproducibility of the deformation behavior for cycles 2–4 highlights the robustness and self-healing nature of these membranes.
4.2. Mechanical characterization of gradient copolymer membranes The mechanical behavior of the G92 crosslinked membranes is not only inuenced by the initial crosslinked network, but also by the adsorption/desorption of the uncrosslinked copolymer, and the continuous self-healing of the carboxylate-ligand linkages. Since the pendant drop remains in an aqueous zinc rich environment it is possible for old crosslinks to repair or restructure, and for new crosslinks to form. The specic time scale for these crosslinking events is expected to be relatively rapid, and the reproducibility of the cycling behavior suggests that the three minute gap between expansion cycles is sufficient
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Fig. 11 Sequential expansion–compression cycles of G92 ionically crosslinked pendant drops (20 minute incubation time). The time between each cycle was approximately three minutes.
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have a well-dened stress plateau. Evidence of possible network damage near the capillary edge was visibly observed around this transition point, supporting this yielding description. Despite this damage, a second expansion–compression cycle follows a nearly identical trend due to the self-healing ability of these membranes. 4.3. Liquid exchange and membrane permeation
Fig. 12 Sequential expansion cycles of G92 ionically crosslinked pendant drops (30 minute incubation time). The time between cycles was approximately three minutes.
Alteration of the fabrication procedure, specically the incubation time (the time between drop formation and initial crosslinking), signicantly inuences the mechanical properties of these membranes. Increasing the incubation time from 20 minutes to 30 minutes leads to a higher surface coverage of gradient copolymers, evident by the lower interfacial tension at the time of initial crosslinking. The excess surface stress behavior of G92 copolymer membranes incubated for 30 minutes is shown in Fig. 12. Here we see that a distinctive linear region denes the initial expansion, followed by plateauing at larger extensions. Similar behavior has been described previously,22 as a linear elastic region, followed by yielding and plasticity. In the linear elastic region, k z 60 mN m1, consistent with a more tightly crosslinked interface compared to the 20 minute incubated membranes. While the membranes formed from shorter incubation times experience a gradual yielding, these membranes undergo an abrupt yielding and
(a–c): Images taken of a water drop placed inside an oil pendant drop containing uncrosslinked gradient copolymers (the embedding phase is water). In less than two seconds, the inside water drop contacts the aqueous interface and bursts out. (d–f) If gradient copolymers are first crosslinked at the outer interface, the inside water droplet can be punched hard into the interface without breaking it. (g) As the chloroform phase evaporates, the inner water drop gets in full contact with the original interface. The crosslinked membrane now becomes a barrier between the water–water interface.
Fig. 13
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Due to the mechanical robustness of the crosslinked membrane, we were able to carry out some more complex manipulations on the interface without destroying the membrane, as shown in Fig. 13(d–f). Here we use a 1 : 1 (weight percentage) mixed solvent of chloroform and toluene to dissolve the gradient copolymer sample, and crosslink the membrane on top of a open-end glass tube in the water embedding phase. When the crosslinked membrane was formed, a needle is inserted into the glass tube to create a bubble of water inside the mixed chloroform–toluene solvent. The water bubble initially stays on the upper part of the oil drop because of the density difference between the oil and water phases. Over the time chloroform dissolves preferentially in the embedding phase, decreasing the density of the mixed solvent. Thus the water bubble eventually sinks to the bottom and comes into contact with the cross-linked membrane (Fig. 13g). This allows us to create a water/membrane/water geometry, which is ideal for future tests such as permeation and ltration.
5.
Conclusion
Here we demonstrated a method for ionically crosslinking amphiphilic copolymers at an oil–water interface and characterized the mechanical properties of the membranes that formed. The key results can be summarized as follows: Ionically crosslinked gradient copolymers formed durable membranes that maintained their physical integrity through multiple expansion–compression–expansion cycles. In contrast, ionically crosslinked block copolymer membranes were critically damaged aer one expansion cycle. This result is attributed to the fact that gradient copolymers are more effective interfacial modiers and have a signicantly different molecular alignment at the oil–water interface. Fluid interface analysis and elastic interface analysis were used to t the interfacial tension of an ionically crosslinked gradient copolymer membrane. The two models had similar prole tting errors and predicted similar trends in the interfacial tension behavior, with the closest agreement occurring in the prediction of Tx at the capillary edge. Due to the comparable results given by the models and the simplicity of the Young– Laplace tting routine, uid interface analysis was used for further mechanical characterization. By changing the incubation time with the copolymer solution from 20 to 30 minutes, the low-strain dilatational modulus of these membranes was signicantly increased due to higher interfacial coverage and crosslinking density. Longer incubation times also led to a distinct yield point and plastic deformation behavior at larger strains.
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The reproducible deformation behavior of these membranes is partially attributed to the reversible nature of ionic crosslinks which allowed these membranes to self-heal.
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Acknowledgements This work was supported by the Petroleum Research Fund, the NSF MRSEC program (DMR-0520513), and the National Institutes of Health under Grant 5R37DE014193-08. Fellowship support from 3M to W. Yuan and from NSF to Kevin J. Henderson is gratefully acknowledged. We are grateful to J. M. Torkelson and M. Mok for providing the gradient copolymers.
References 1 J.-Y. Sun, X. Zhao, W. R. K. Illeperuma, O. Chaudhuri, K. H. Oh, D. J. Mooney, J. J. Vlassak and Z. Suo, Nature, 2012, 489, 133–136. 2 S. E. Bakarich, G. C. Pidcock, P. Balding, L. Stevens, P. Calvert and M. I. H. Panhuis, So Matter, 2012, 8, 9985– 9988. 3 A. N. J˘ atariu (Cadinoiu), M. Popa, S. Curteanu and C. A. Peptu, J. Biomed. Mater. Res., Part A, 2011, 98, 342–350. 4 K. J. Henderson, T. C. Zhou, K. J. Otim and K. R. Shull, Macromolecules, 2010, 43, 6193–6201. 5 D. A. Devi, B. Smitha, S. Sridhar and T. Aminabhavi, Sep. Purif. Technol., 2006, 51, 104–111. 6 R. Y. M. Huang and J.-J. Shieh, Sep. Sci. Technol., 1997, 32, 2765–2784. 7 T.-M. Don, M.-L. Huang, A.-C. Chiu, K.-H. Kuo, W.-Y. Chiu and L.-H. Chiu, Mater. Chem. Phys., 2008, 107, 266–273. 8 J. V. Gasa, R. Weiss and M. T. Shaw, J. Membr. Sci., 2007, 304, 173–180. 9 J. Kerres, W. Zhang, A. Ullrich, C.-M. Tang, M. Hein, V. Gogel, T. Frey and L. J¨ orissen, Desalination, 2002, 147, 173–178. 10 J. A. Kerres, Fuel Cells, 2005, 5, 230–247. 11 M. A. Bos and T. van Vliet, Adv. Colloid Interface Sci., 2001, 91, 437–471. 12 E. Boucher and H. Kent, J. Colloid Interface Sci., 1978, 67, 10– 15.
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13 M. A. Cabrerizo-V´ılchez, H. A. Wege, J. A. Holgado-Terriza and A. W. Neumann, Rev. Sci. Instrum., 1999, 70, 2438– 2444. 14 M. D. Lefebvre, R. L. McSwain, C. M. Dettmer, C. Xu, J. R. Davila, R. J. Composto, S. T. Nguyen and K. R. Shull, Macromolecules, 2005, 38, 10494–10502. 15 L. Leibler, H. Orland and J. Wheeler, J. Chem. Phys., 1983, 79, 3550. 16 R. W. Sandoval, D. E. Williams, J. Kim, C. B. Roth and J. M. Torkelson, J. Polym. Sci., Part B: Polym. Phys., 2008, 46, 2672–2682. 17 K. Shull, Macromolecules, 2002, 35, 8631–8639. 18 W. Yuan, M. M. Mok, J. Kim, C. L. H. Wong, C. M. Dettmer, S. T. Nguyen, J. M. Torkelson and K. R. Shull, Langmuir, 2010, 26, 3261–3267. 19 C. L. H. Wong, J. Kim and J. M. Torkelson, J. Polym. Sci., Part B: Polym. Phys., 2007, 45, 2842–2849. 20 P. Erni, H. A. Jerri, K. Wong and A. Parker, So Matter, 2012, 8, 6958–6967. 21 J. K. Ferri, W.-F. Dong, R. Miller and H. M¨ ohwald, Macromolecules, 2006, 39, 1532–1537. 22 J. K. Ferri, C. Kotsmar and R. Miller, Adv. Colloid Interface Sci., 2010, 161, 29–47. 23 N. A. Alexandrov, K. G. Marinova, T. D. Gurkov, K. D. Danov, P. A. Kralchevsky, S. D. Stoyanov, T. B. Blijdenstein, L. N. Arnaudov, E. G. Pelan and A. Lips, J. Colloid Interface Sci., 2012, 376, 296–306. 24 Z. Kang, A. Yeung, J. M. Foght and M. R. Gray, Colloids Surf., B, 2008, 62, 273–279. 25 J. K. Ferri, P. A. L. Fernandes, J. T. McRuiz and F. Gambinossi, So Matter, 2012, 8, 10352–10359. 26 D. Carvajal, E. J. Laprade, K. J. Henderson and K. R. Shull, So Matter, 2011, 7, 10508. 27 R. Long, K. R. Shull and C.-Y. Hui, J. Mech. Phys. Solids, 2010, 58, 1225–1242. 28 J. K. Ferri and P. A. L. Fernandes, in Bubble and Drop Interfaces, ed. R. Miller, L. Liggieri and E. J. Brill, Leiden, Netherlands, 2011, vol. 2, pp. 61–74. 29 R. Wang, W. Li, Y. Luo, B.-G. Li, A.-C. Shi and S. Zhu, Macromolecules, 2011, 42, 2275–2285.
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PAPER
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Formation and mechanical characterization of ionically crosslinked membranes at oil–water interfaces Wa Yuan, Evan J. Laprade, Kevin J. Henderson and Kenneth R. Shull* Here we report on the preparation and mechanical characterization of a 2-D self-assembled membrane formed by ionically crosslinking the polyelectrolyte parts of a gradient amphiphilic copolymer at oil and water interfaces. To fabricate these membranes, chloroform solutions of styrene–acrylic acid copolymers were suspended as pendant drops in an aqueous embedding phase. Due to the amphiphilic nature of these molecules, the copolymer chains migrate to the oil–water interface creating an interfacial layer. Upon the addition of zinc acetate to the embedding phase, crosslinks between copolymer molecules are formed via zinc–carboxylate complexes. While ionically crosslinked block copolymer membranes were critically damaged after one expansion cycle, ionically crosslinked gradient copolymers formed durable membranes that maintained their physical integrity through multiple expansion–compression–expansion cycles. This difference in mechanical behavior is attributed to the fact that gradient copolymers are more effective interfacial modifiers and have a significantly different molecular alignment at the oil–water interface. Additionally by changing the incubation time from 20 to 30 minutes, the low-strain dilatational modulus of these membranes was significantly increased due to
Received 16th July 2013 Accepted 25th October 2013
higher interfacial coverage and crosslinking density. Longer incubation times also led to a distinct yield point and plastic deformation behavior at larger strains. Further mechanical characterization of the
DOI: 10.1039/c3sm51943k
membranes showed that they can be quite robust and that by replacing the internal oil phase with an
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aqueous solution, future testing of membrane filtration and permeation may be possible.
1. Introduction Ionically crosslinked networks are oen incorporated into covalently crosslinked polymers to enhance their mechanical and transport properties.1–4 In polymer bulk gels for instance, the addition of a second, tightly cross-linked network assists in broadening the fracture zone and maximizing dissipation, creating so materials with fracture energies comparable to or exceeding that of natural biomaterials.1 Additionally, the reversibility of these bonds provides these gels with a remarkable ability to recover aer plastic deformation, giving them a self-healing character.2 Ionic crosslinking of two dimensional structures is equally attractive, as it can be used to tailor the membrane permeability and permselectivity for liquid phase transport applications. In recent work, these lms have increasingly been targeted as membranes for liquid mixture separation,5,6 drug delivery7 and fuel cells.8–10 Looking towards these goals, we introduce a simple way of preparing and mechanically characterizing free standing ionically crosslinked polymer membranes. Northwestern University Materials Science and Engineering, 2220 Campus Drive, Evanston, Illinois, USA. E-mail: [email protected]; Fax: +1 8474917820; Tel: +1 8474671752
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The most frequently used technique to produce ionic crosslinking is by complexation of multi-valent cations and carboxylate ligands, in what is predominantly an electro-static interaction. In our experiments, pendant drop membranes
Fig. 1 Formation of ionically crosslinked interfacial layers: (left) gradient copolymers dissolved in chloroform adsorb onto the interface of a pendant drop at the tip of a capillary needle. The embedding phase is pure water. The inset shows an idealized orientation of gradient copolymers at the oil–water interface. (right) Zinc acetate solution is added to the aqueous embedding phase. The inset shows divalent ion-carboxylate ligand complexing at the interface, creating an ionically crosslinked membrane.
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2.
Materials and methods
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2.1. Materials
Fig. 2 (a) Schematic structure of a styrene/acrylic acid gradient copolymer. Carboxylate ligands replace aqua ligands in the inner sphere of a Zn ionic complex. Schematic structure of styrene (b) and (c) acrylic acid.
were formed through zinc(II) crosslinking of an amphiphilic styrene/acrylic acid gradient copolymer (Fig. 2) at an oil–water interface as shown in Fig. 1. The pendant drop technique is a commonly used method for characterizing the mechanical properties of two dimensional structures that self-assemble at uid–uid interfaces. While being conceptually more complex than at interface techniques,11–13 a pendant drop technique can offer several important advantages due to its small reagent volumes and rapid equilibration times. The interfacial tension between the drop and the embedding phase can be obtained by analyzing the drop shape, and changing the drop volume allows one to mechanically characterize the interface. The amphiphilic copolymers used here to form crosslinked membranes are referred to as gradient copolymers (Fig. 2). They exhibit a gradual change of composition along the backbone,14 which leads to lower repulsion forces distributed along the chain. It has been shown previously that the molecular structure of gradient copolymers results in a larger critical micelle concentration in polymer blends15–17 and molecular alignment at the oil–water interface that differs signicantly from traditional block copolymers.18 Our work suggests that copolymer membrane formation is facilitated by the reduction of these kinetic barriers and by the specic details of the molecular organization at the interface before crosslinking. In this paper we begin by discussing the materials and methods for fabricating ionically crosslinked pendant drops. Then we summarize the mechanics of the pendant drop geometry, and provide the background necessary to analyze both uid and elastic interfaces. Next we model an ionically crosslinked drop with both analyses, evaluating the t quality and principal tension predictions. The availability of these models puts us in a position to characterize the mechanical behavior of these membranes, look at the effect of processing conditions, and discuss their self-healing ability. Lastly we present preliminary results highlighting how the robust nature of this technique could be used to look at transport through these crosslinked interfaces.
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Styrene–acrylic acid (S/AA) gradient copolymers were synthesized as previously described18 using semi-batch nitroxide mediated controlled radical polymerization (NM-CRP) from the unimolecular initiator alkoxyamine 29 (2,2,5-trimethyl-3(1-phenylethoxy)-4- phenyl-3-azahexane).19 The PS/PtBA precursor copolymers were recovered by cycles of precipitation into methanol and dissolution into tetrahydrofuran before drying under vacuum. For comparison a block copolymer with similar molecular weight was also prepared, using sequential, batch NM-CRP. The nal products were labeled as G92 (Mn ¼ 91 800 g mol1, styrene fraction ¼ 0.55) and B89 (Mn ¼ 88 700 g mol1, styrene fraction ¼ 0.69), according to the copolymer type and number average molecular weight. The nal apparent molecular weights (MWs) and cumulative styrene mole fractions (FS) for the two types of copolymers used for this study are summarized in Table 1. Both copolymers were dissolved in chloroform (CHROMASOLV PLUS, FOR HPLC) at a concentration of 0.02 mg mL1. Dihydrate zinc acetate (as received, Sigma Aldrich) and pure water (A. C. S. REAGENT, Sigma Aldrich) were used to prepare 400 mM zinc acetate solutions. These solutions were buffered with acidic acid to a nal pH of 6, conrmed using a WTW Portable pH Tester, Model 20. 2.2. Drop shape analysis system A commercial drop shape tensiometer (Kr¨ uss DSA 100) was used to image the pendant drop prole. The drop shape analysis video was analyzed with a custom written MATLAB (Mathworks) pendant drop mechanical analysis, outlined in Section 3. The drop volume was controlled via a motor driven syringe system. 2.3. Pendant drop membrane fabrication Interfacial layers were investigated using the pendant drop method and drop-shape analysis (DSA). A 4–6 ml pendant drop of chloroform containing the desired copolymer was formed at the end of the capillary needle (diameter ¼ 0.914 mm) inside a water lled glass cuvette (cuvette dimensions ¼ 1 cm 1 cm 5 cm). Once the pendant drop was formed, it was xed at the initial volume for a period of time (referred to here as the “incubation period”) to allow the copolymers to migrate to the oil and water interface. Aer this incubation period, zinc acetate
Summary of molecular characterization data for gradient (G) and diblock (B) S/AA copolymers
Table 1
Sample
Fs
Mna (g mol1)
PDIa
G92 B89
0.55 0.69
91 800b 88 700c
1.48b 1.79b
a Mn and PDI data based on S/tBA copolymers. b The apparent value characterized relative to PS standards by GPC with THF as an eluent. c The Mn value was determined from the Mn of the PtBA macroinitiator and the Fs value.
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Soft Matter
solution was added to the aqueous imbedding phase to create carboxylate ligand complexation at the interface. The nal concentration of zinc acetate in the aqueous phase was approximately 40 mM. Aer the addition of zinc acetate, the drop was held for approximately ve minutes to form an ionically crosslinked interface. Immediately following this period, the drop volume was decreased slightly to test the formation of the membrane, indicated by wrinkling of the interface. Aer the drop was re-expanded back to the original size, a set of cycles were carried out following a routine of expansion– compression–expansion. Drops were expanded to a 40% increase in interfacial area (relative to the initial drop surface area), compressed to a 20% reduction, and then re-expanded back to the original size. The time between the end of one expansion–compression–expansion cycle and the start of the next was approximately three minutes. All experiments were performed at a xed ow rate of 0.4 mL min1. Before and aer each new experiment, the glass cuvette was thoroughly washed with acetone and water, while the needles and glass syringe were washed with acetone and chloroform. Fig. 3 shows representative images at different stages of expansion and compression for a crosslinked G92 copolymer membrane. We note that the wrinkling wavelength observed during compression is approximately 35–40 mm for the smallest observable wrinkles, and at larger compressions these small wrinkles became larger folds with a wavelength of approximately 100 mm. These wrinkle wavelengths are quite similar to those observed by Erni et al.20 for oil–water emulsion drops exhibiting shear elasticity.
3.
Membrane mechanics
3.1. Theoretical background DSA is most commonly used to measure the interfacial tension between two immiscible uids, but has increasingly been employed to characterize the mechanical behavior of molecular structures that self-assemble at these interfaces.20–24 General theoretical frameworks that encompass these solid-like interfaces have been summarized recently,25,26 here we follow the formulation given by Carvajal et al.26
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Fig. 4 Schematic representation of an axisymmetric pendant drop.
In Fig. 4, we dene a coordinate system for the pendant drop geometry with its origin at the drop apex. The arc length of the interface between the two phases s runs from the apex (s ¼ 0) to the capillary edge (s ¼ l), where l is the total integrated arc length. The shape of the pendant drop interface is dened by its principal curvatures Rx and Rf, the curvatures in the r z plane and in the azimuthal direction respectively. The principal curvatures are dened as ds da
(1)
r sin a
(2)
Rx ¼ Rf ¼
where the quantity a(s) is the angle between the tangent to the interface at [r(s), z(s)] and the radial axis. In the most general case of an elastic or solid-like interface, the pendant drop geometry is governed by force balances in the direction normal to the interface, and along the x principal direction (a force balance in the f direction is satised by the axisymmetry of the problem). From the normal force balance one can derive the Young–Laplace relationship: DP ¼
Tx Tf þ Rx Rf
where the principal tensions, Tx and Tf, and local curvatures balance the pressure difference across the interface, DP. It can be shown that the mechanical equilibrium equation for the x direction is given by: d ðTx rÞ ¼ Tf dr
Images of the crosslinked G92 copolymer membrane (20 minute incubation) during the 1st expansion–compression–expansion cycle. The left image corresponds to A/A0 ¼ 1, where A0 is the drop surface area at the beginning of the cycle. The center image corresponds to A/A0 ¼ 1.39 (the maximum surface area during the cycle). The right image corresponds to a deep compressed state (A/A0 ¼ 0.81) where wrinkling can be observed in the upper portion of the drop interface. Fig. 3
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(3)
(4)
In the case of a purely uid interface, which is unable to support shear stresses, the principal tensions are spatially uniform and equal, Tx ¼ Tf ¼ g. Eqn (4) is automatically satised, and the interfacial tension can be measured by simply tting the Young–Laplace equation to the drop prole. An elastic or solid interface presents a more complicated situation where the principal tensions are no longer isotropic and instead will depend on the local in-plane principal strains, lx and lf. For an elastic interface we assume that the principal tensions consist of a pretension component g0 , equal to the interfacial tension of the pendant drop in the undeformed state, and an elastic component, which is determined by the strain energy per unit area of the undeformed membrane, U.
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T x ¼ g0 þ
1 vU lf vlx
(5)
T f ¼ g0 þ
1 vU lx vlf
(6)
A neo-Hookean strain energy function is commonly chosen as a general description of elasticity,27 and here we use it to derive the following expressions for the principal tensions: ! Eh0 lx 1 0 Tx ¼ g þ (7) 3 lf lx 3 lf 3 Eh0 Tf ¼ g þ 3 0
lf 1 lx lx 3 lf 3
! (8)
where Eh0 is the low-strain dilatational modulus, E is Young’s elastic modulus, and h0 is the undeformed thickness of the membrane. Eqn (7) and (8) were derived under the assumption of incompressibility. In Section 3.4 we utilize both the uid interface analysis (eqn (3)) and the elastic interface analysis (eqn (3)–(8)) to characterize the mechanical behavior of a crosslinked gradient copolymer pendant drop. 3.2. Fluid interface tting Isotropic interfacial tension values were determined using a modied version of the Young–Laplace tting routine previously described by Carvajal et al.26 To briey summarize, eqn (1)–(3) are combined with the geometrical relationships, dr/ds ¼ cos a and dz/ds ¼ sin a, to give three coupled rst order differential equations (for a, r and z) that describe the pendant drop’s conguration. We specify ve boundary conditions: three at the drop apex and two at the capillary needle edge. In order for all ve boundary conditions to be met, two parameters must be allowed to oat. These parameters are the interfacial tension, g, and the pressure at the apex, P0. A custom MATLAB script was used to digitize the drop prole, solve the differential equations, and adjust the parameters to determine which value of g minimizes the error, Lres, in prole tting. This error is dened in the following way: Lres ¼
N 1 X di ; NRm i¼1
(9)
where di is the normal distance between the model and the experimental prole at each model prole point (r(i), z(i)), Rm is the radius of the membrane holder, and N is the total number of points along the prole. Note that Lres is the average distance between the actual drop prole and the t to the droplet shape from the solution to the equations in the previous section, normalized by Rm. 3.3. Elastic interface tting For the elastic case we need to solve a total of four differential equations, for a, z lx, and lf. There are a total of six boundary conditions to be met, so two parameters must be allowed to
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oat, and these parameters are the pressure at the apex of the deformed membrane, and Eh0, the low strain dilatational modulus. Our use of Eh0 as an adjustable parameter is not a rigorous treatment of viscoelasticity, but this method provides a simple rst order approximation of the time-dependent modulus of the membranes. To analyze an elastic interface we make the assumption that a pendant drop with a liquid-like interfacial layer has undergone crosslinking, forming an elastic membrane at the interface. This undeformed, yet crosslinked pendant drop is dened as the reference conguration. It is assumed that in this undeformed state, the principal tensions are spatially uniform and equal to one another, Tx ¼ Tf ¼ g0 . Subsequent deformation of the drop changes the local values of lx and lf and therefore the elastic contributions to the principal tensions. We begin by determining g0 , analyzing an image of the undeformed drop with the uid interface analysis. Aer determining g0 , the elastic drop analysis can be used to model the deformation of drop starting with expansion. A custom MATLAB script was used to digitize the drop prole, solve the differential equations, and adjust the parameters to minimize the error, Lres.
3.4. Fluid and elastic interface analysis comparison The uid to elastic transition of pendant drop interfaces can be monitored by examining the error in tting the Young–Laplace equation to the interface shape.23,25,28 As the drop becomes more solid-like there will be an increase in the error that can provide a signature of the formation of an elastic interface with nonuniform tension. The use of an approximate “uid interface” model that assumes a uniform, isotropic tension is motivated by the simplicity of the tting routines that are generally available for commercial pendant drop instruments. An important question that needs to be addressed in these situations is how closely this uid interface analysis approximates the true interfacial tension. In this section we examine the agreement between the elastic and uid interface analyses for our crosslinked pendant drops, specically looking at the quality of the prole ts and at the magnitude and spatial variation of the interfacial tensions. Following the procedure outlined in Sections 3.2 and 3.3, uid and elastic interface analyses were applied to the expansion and compression cycle of a G92 gradient copolymer pendant drop. During the 20 minute incubation period, the drop interface has a uid-like character, and we expect excellent agreement between the interface shape and the Young–Laplace solution. We can use the average value of the tting error in this regime (Lres ¼ 0.0025), as a reference for what constitutes a quality t. In Fig. 5, this average tting error for the uncrosslinked drop is plotted as a solid black line, along with the tting error for the uid and elastic interface analyses during the expansion and compression of the crosslinked G92 gradient copolymer pendant drop. Both analyses produce comparable residuals over the majority of deformations. In both cases the error is comparable to our reference value until the drop is compressed back to an areal dilatation of A/A0 ¼ 1, where A is the actual interfacial area and A0 is the original interfacial area
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Fig. 5 Left axis: the fitting error, Lres, for the fluid and elastic analysis fits to the pendant drop profile. This measurement was the first expansion–compression cycle of an ionically crosslinked G92 membrane (20 minute incubation period). The solid black line corresponds to the average fitting error for the uncrosslinked G92 pendant drop. Right axis: areal dilatation versus experiment time.
for that specic cycle. Further compression results in poor tting for both cases, particularly as the membrane begins to wrinkle (A/A0 < 0.95), and the tting error sharply increases. As
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neither model correctly interprets the tensions in this regime, we restrict our analysis to A/A0 > 0.95 in the work that follows. The prole ts and local residuals at interfacial area extensions A/A0 ¼ 1.09 (time ¼ 110 s) and A/A0 ¼ 1.29 (time ¼ 548 s) are shown in Fig. 6a, c and (d)–(f) respectively. For both of these deformations the uid interface, elastic interface, and experimental proles are nearly indistinguishable from one another (Fig. 6a and d) and small differences only become clear when looking at the local residuals (Fig. 6b and e). More signicant differences between the models are evident in the principal tension behavior, Fig. 6c and f, particularly in the spatial distribution of the principal tensions. The additional boundary conditions for the elastic interface analysis lead to an anisotropic strain state, with the boundary condition lx(s ¼ 0) ¼ lf(s ¼ 0) forcing equibiaxial tension at the drop apex and the boundary condition lf(s ¼ l) ¼ 1 diverging the principal tensions at the capillary edge. Our analysis of the G92 crosslinked interface shows a small deviation between the elastic tensions and g, as depicted in Fig. 7 and 8. Interestingly, despite the very close agreement between the uid and elastic prole shapes, the interfacial tension, g, does not necessarily fall somewhere in between the predictions for Tx and Tf. At the apex, the uid analysis slightly overestimates the tension, as shown in Fig. 7, and similarly
Fluid and elastic interface analysis results for the first expansion–compression cycle of a G92 copolymer membrane (20 minute incubation time). Plots (a–c) correspond to A/A0 ¼ 1.09, time ¼ 110 s. Plots (d–f) correspond to A/A0 ¼ 1.29, time ¼ 548 s. Left plots (a and d) show the measured membrane profile prior to expansion (undeformed membrane, gray solid line) and the experimentally measured membrane profile at A/A0 (deformed membrane, green solid line). The fluid model fit to the deformed membrane profile (black dashed line), and the elastic model fit to the deformed membrane profile (blue dashed line) are nearly indistinguishable from themselves and the measured deformed membrane profile. The center plot (b and e) shows the residual errors di/Rm, along the membrane profile from the fluid and elastic interface analysis. Right plots (c and f) compare the principal tensions given by the elastic analysis to the interfacial tension, g, measured by the fluid analysis. Note that these x-axes run from the membrane apex, s/l ¼ 0, to the clamp edge, s/l ¼ 1. Fig. 6
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deviations between the elastic and uid tting routines to be more pronounced. We used the uid model to analyze all of the data discussed in the following sections.
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4. Results and discussion 4.1. Block and gradient copolymer membrane deformation
Fig. 7 Apex interfacial tension (IFT) plotted as a function of areal dilatation for the first expansion–compression cycle of a crosslinked G92 copolymer membrane (20 minute incubation time). The solid arrow represents the direction of the curve during expansion and the dashed arrow represents the direction of the curve during compression. The fluid interface analysis was used to calculate g, and the elastic interface analysis was used to calculate the tension at the apex. Note Tx(s ¼ 0) ¼ Tf(s ¼ 0) ¼ Tapex.
As described above, the G92 gradient copolymer was dissolved in chloroform at a concentration of 0.02 mg mL1, and this solution was used to form a pendant drop at the tip of a capillary needle submerged in water. During the incubation period the interfacial tension decreased signicantly from that of pure chloroform/water (32.8 mN m1). Aer a 20 minute incubation period g decreased approximately to 17 mN m1, and aer a 30 minute incubation period g decreased approximately to 10 mN m1. Additionally during this incubation time, the initially clear drop became more cloudy in appearance. Aer the addition of zinc acetate, the G92 drop was compressed and wrinkling was clearly observed, indicating the formation of a crosslinked membrane at the oil–water interface. In each subsequent expansion–compression cycle wrinkling was always observed during compression. Fig. 9 shows a comparison between an expansion–compression cycle of interfaces with and without cross-linking on exposure to zinc acetate. Droplets formed by B89 on the other hand showed a significantly smaller decrease in interfacial tension in these incubation periods compared to G92 gradient copolymers. This observation was consistent with our previous results which showed that in a limited time scale block copolymers are less efficient at going to the oil–water interface due to kinetic barriers associated with micelle aggregation in the chloroform phase.18 The coverage of copolymers at the interface was not sufficient to form a uniform membrane, and thus droplets formed by B89 did not show a clear sign of wrinkling during compression. To further compare, we increased the concentration of B89 solution to 0.1 mg mL1 and extended the
Fig. 8 Interfacial tension (IFT) at the capillary edge (z(s ¼ 1) ¼ d) plotted as a function of areal dilatation for the first expansion–compression cycle of a crosslinked G92 copolymer membrane (20 minute incubation time). The fluid interface analysis was used to calculate g, and the elastic interface analysis was used to calculate the principal tensions at the capillary edge.
overestimates Tf at the capillary edge, as shown in Fig. 8. The best agreement between the uid and elastic analyses can be found in their prediction of Tx at the capillary edge, where the tensions track closely until A/A0 z 1.08, at which point the tting error for both analyses begins to signicantly increase. While the deviations between the elastic and uid interface analyses are non-trivial, a good agreement exists between the two, particularly for g and Tx at z ¼ d. These observations suggest that in our case, the simpler, and more tractable uid analysis can provide a useful approximation of the interfacial tension. For more strongly crosslinked interfaces with higher stiffness and less healing capability,25 one would expect the
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Fig. 9 Comparison of interfacial tension behavior between G92 uncrosslinked (blue circles) and crosslinked (black squares) layers during expansion–compression. Dashed arrows represent the direction of curve during compression and solid arrows represent the direction of the curve during expansion.
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for new crosslinks to form. The deformation shown in Fig. 9 is a characteristic cycle (in this case the rst cycle) for a G92 membrane incubated for 20 minutes. At small strains there is an initial linear section where we can characterize the stiffness of these membranes by measuring the dilatational modulus, k, dened as follows: dg k ¼ A0 (10) dA
Schematic illustration of the proposed interfacial structure evolution of crosslinked block and gradient copolymer membranes under an applied tensile force.
Fig. 10
incubation time to 3 hours. Under this condition the interface did show a sign of wrinkling during the compression process, indicating the formation of a crosslinked membrane. However, when we expanded the drop by 20% and re-compressed it, the wrinkling phenomenon was no longer observed, indicating damage of the membrane during expansion. Fig. 10 shows a schematic representation of the proposed cross-linking processes for the two types of copolymers. For block copolymers, the junction points between blocks of the hydrophobic and hydrophilic monomers are localized at the oil–water interface, forming a brush-like structure. The addition of zinc ions to the aqueous phase crosslinks this entangled brush layer. When the interface is expanded, a tensile force is applied to the crosslinked layer pulling the block copolymers apart, and breaking the membrane. Gradient copolymers on the other hand have multiple hydrophilic/hydrophobic junction points along the chain which may result in a more “parallel” structure, with the molecules laterally extended along the interface.17,18,29 Aer the addition of zinc these “parallel” chains form a more complex network of intermolecular cross-links, resulting in the formation of a stronger membrane. When this membrane is placed under a similar tensile force, the “parallel” molecules do not simply detach from each other, but rather extend and uncoil. This helps maintaining the physical integrity of the membrane and enables the membrane to be expanded to twice its original area.
The small strain stiffness for this rst expansion cycle was k z 47 mN m1, signicantly higher than that of the uncrosslinked layer, k z 14 mN m1. While the dilatational modulus remains fairly constant for the uncrosslinked interface in Fig. 7, as the membrane is expanded to larger strains the slope of the interfacial tension curve decreases. Our explanation for this soening behavior is a combination of damage to the crosslinked network (local crosslink fracture, rather than catastrophic failure), and also adsorption of the uncrosslinked copolymer onto the expanded interface. As the drop is compressed back to its original size, uncrosslinked copolymer de-adsorption from the interface contributes to the signicant hysteresis between the expansion and compression cycles. Aer the drop is compressed back to its original interfacial area, the three minute incubation time in between cycles allows the fractured interface to repair and for new crosslinks to form. If we consider the beginning of each cycle to be like the formation of a new crosslinked membrane, we can characterize the excess surface stress, s, for each cycle: s ¼ g g0
(11)
where g0 is the interfacial tension at the beginning of each specic cycle. In Fig. 11, s is plotted as a function of A/A0 for the rst four deformation cycles of the crosslinked G92 copolymer aer a 20 minute incubation. The small strain expansion is comparable for all cycles, characterized by an average k value of 45 mN m1. The reproducibility of the deformation behavior for cycles 2–4 highlights the robustness and self-healing nature of these membranes.
4.2. Mechanical characterization of gradient copolymer membranes The mechanical behavior of the G92 crosslinked membranes is not only inuenced by the initial crosslinked network, but also by the adsorption/desorption of the uncrosslinked copolymer, and the continuous self-healing of the carboxylate-ligand linkages. Since the pendant drop remains in an aqueous zinc rich environment it is possible for old crosslinks to repair or restructure, and for new crosslinks to form. The specic time scale for these crosslinking events is expected to be relatively rapid, and the reproducibility of the cycling behavior suggests that the three minute gap between expansion cycles is sufficient
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Fig. 11 Sequential expansion–compression cycles of G92 ionically crosslinked pendant drops (20 minute incubation time). The time between each cycle was approximately three minutes.
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have a well-dened stress plateau. Evidence of possible network damage near the capillary edge was visibly observed around this transition point, supporting this yielding description. Despite this damage, a second expansion–compression cycle follows a nearly identical trend due to the self-healing ability of these membranes. 4.3. Liquid exchange and membrane permeation
Fig. 12 Sequential expansion cycles of G92 ionically crosslinked pendant drops (30 minute incubation time). The time between cycles was approximately three minutes.
Alteration of the fabrication procedure, specically the incubation time (the time between drop formation and initial crosslinking), signicantly inuences the mechanical properties of these membranes. Increasing the incubation time from 20 minutes to 30 minutes leads to a higher surface coverage of gradient copolymers, evident by the lower interfacial tension at the time of initial crosslinking. The excess surface stress behavior of G92 copolymer membranes incubated for 30 minutes is shown in Fig. 12. Here we see that a distinctive linear region denes the initial expansion, followed by plateauing at larger extensions. Similar behavior has been described previously,22 as a linear elastic region, followed by yielding and plasticity. In the linear elastic region, k z 60 mN m1, consistent with a more tightly crosslinked interface compared to the 20 minute incubated membranes. While the membranes formed from shorter incubation times experience a gradual yielding, these membranes undergo an abrupt yielding and
(a–c): Images taken of a water drop placed inside an oil pendant drop containing uncrosslinked gradient copolymers (the embedding phase is water). In less than two seconds, the inside water drop contacts the aqueous interface and bursts out. (d–f) If gradient copolymers are first crosslinked at the outer interface, the inside water droplet can be punched hard into the interface without breaking it. (g) As the chloroform phase evaporates, the inner water drop gets in full contact with the original interface. The crosslinked membrane now becomes a barrier between the water–water interface.
Fig. 13
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Due to the mechanical robustness of the crosslinked membrane, we were able to carry out some more complex manipulations on the interface without destroying the membrane, as shown in Fig. 13(d–f). Here we use a 1 : 1 (weight percentage) mixed solvent of chloroform and toluene to dissolve the gradient copolymer sample, and crosslink the membrane on top of a open-end glass tube in the water embedding phase. When the crosslinked membrane was formed, a needle is inserted into the glass tube to create a bubble of water inside the mixed chloroform–toluene solvent. The water bubble initially stays on the upper part of the oil drop because of the density difference between the oil and water phases. Over the time chloroform dissolves preferentially in the embedding phase, decreasing the density of the mixed solvent. Thus the water bubble eventually sinks to the bottom and comes into contact with the cross-linked membrane (Fig. 13g). This allows us to create a water/membrane/water geometry, which is ideal for future tests such as permeation and ltration.
5.
Conclusion
Here we demonstrated a method for ionically crosslinking amphiphilic copolymers at an oil–water interface and characterized the mechanical properties of the membranes that formed. The key results can be summarized as follows: Ionically crosslinked gradient copolymers formed durable membranes that maintained their physical integrity through multiple expansion–compression–expansion cycles. In contrast, ionically crosslinked block copolymer membranes were critically damaged aer one expansion cycle. This result is attributed to the fact that gradient copolymers are more effective interfacial modiers and have a signicantly different molecular alignment at the oil–water interface. Fluid interface analysis and elastic interface analysis were used to t the interfacial tension of an ionically crosslinked gradient copolymer membrane. The two models had similar prole tting errors and predicted similar trends in the interfacial tension behavior, with the closest agreement occurring in the prediction of Tx at the capillary edge. Due to the comparable results given by the models and the simplicity of the Young– Laplace tting routine, uid interface analysis was used for further mechanical characterization. By changing the incubation time with the copolymer solution from 20 to 30 minutes, the low-strain dilatational modulus of these membranes was signicantly increased due to higher interfacial coverage and crosslinking density. Longer incubation times also led to a distinct yield point and plastic deformation behavior at larger strains.
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The reproducible deformation behavior of these membranes is partially attributed to the reversible nature of ionic crosslinks which allowed these membranes to self-heal.
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Acknowledgements This work was supported by the Petroleum Research Fund, the NSF MRSEC program (DMR-0520513), and the National Institutes of Health under Grant 5R37DE014193-08. Fellowship support from 3M to W. Yuan and from NSF to Kevin J. Henderson is gratefully acknowledged. We are grateful to J. M. Torkelson and M. Mok for providing the gradient copolymers.
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